The method of upper-lower solutions for nonlinear second order differential inclusions

Papageorgiou, NS; Staicu, V

dc.contributor.author	Papageorgiou, NS	en
dc.contributor.author	Staicu, V	en
dc.date.accessioned	2014-03-01T01:27:26Z
dc.date.available	2014-03-01T01:27:26Z
dc.date.issued	2007	en
dc.identifier.issn	0362-546X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/18447
dc.subject	Extremal solutions	en
dc.subject	Fixed points	en
dc.subject	Multifunctions	en
dc.subject	Truncation and penalty functions	en
dc.subject	Upper and lower solutions	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Mathematics	en
dc.subject.other	Boundary value problems	en
dc.subject.other	Laplace equation	en
dc.subject.other	Nonlinear equations	en
dc.subject.other	Perturbation techniques	en
dc.subject.other	Theorem proving	en
dc.subject.other	Extremal solutions	en
dc.subject.other	Fixed points	en
dc.subject.other	Penalty functions	en
dc.subject.other	Upper and lower solutions	en
dc.subject.other	Differential equations	en
dc.title	The method of upper-lower solutions for nonlinear second order differential inclusions	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.na.2006.06.023	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.na.2006.06.023	en
heal.language	English	en
heal.publicationDate	2007	en
heal.abstract	In this paper we consider a second order differential inclusion driven by the ordinary p-Laplacian, with a subdifferential term, a discontinuous perturbation and nonlinear boundary value conditions. Assuming the existence of an ordered pair of appropriately defined upper and lower solutions phi and psi respectively, using truncations and penalization techniques and results from nonlinear and multivalued analysis, we prove the existence of solutions in the order interval [psi, phi] and of extremal solutions in [psi, phi]. We show that our problem incorporates the Dirichlet, Neumann and Sturm-Liouville problems. Moreover, we show that our method of proof also applies to the periodic problem. (C) 2006 Elsevier Ltd. All rights reserved.	en
heal.publisher	PERGAMON-ELSEVIER SCIENCE LTD	en
heal.journalName	Nonlinear Analysis, Theory, Methods and Applications	en
dc.identifier.doi	10.1016/j.na.2006.06.023	en
dc.identifier.isi	ISI:000246772400004	en
dc.identifier.volume	67	en
dc.identifier.issue	3	en
dc.identifier.spage	708	en
dc.identifier.epage	726	en